We are going to focus just on the precession,
that is, we are going to focus on the coordinate , first in the classical way, and then by using the length and time equations
derived in the previous post “The gem (1)”.

So, let’s do it.

Classical calculation:

- position of the planet

- velocity

– kinetic energy

– gravitational potential energy

( is the well known constant of motion: the angular
momentum)

So, by using the classical calculation, we’ve
got that

But, when we take into account the
gravitational influence (derived in the previous post “The gem (1)”), we have:

By
applying the classical calculation, we’ve got that Let’s denote the \phi
in the classical calculation as . So,

In the classical case, there is no
precession:

But, in this case (where we’ve used the
length and time equations derived in the previous post “The gem (1)”), we have
the precession, and it can be calculated as: